If \frac{3}{x+3}+\frac{4}{x+4}=\frac{2}{x+2}+\frac{5}{x+5}, then the value of x is
A. \frac {13}{4}
B. -\frac {5}{2}
C. -\frac {7}{2}
D. \frac {9}{2}
E. \frac {17}{2}
Can someone kindly help me in answering this question. The source of this question is Jumbo Tests.
Thanks in advance.
SD
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Quadratic Equation Problem
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It is a little hard to understand the notations. Can you rewrite or potentially use an image?
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jitsy
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Could anyone solve this ques. The only thing I can figure out is that in the ques itself, in a way, 3 and 4 have been written as 2+1 and 5-1 which becomes 2+5 (if you know what I mean). Experts?
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Hi everyone,
I think that the question is supposed to be this:
3/(x+3) + 4/(x+4) = 2/(x+2) + 5/(x+5) x = ?
13/4
-5/2
-7/2
9/2
17/2
I've come to a solution by using the following math steps:
First, set a common denominator for the left and a separate common denominator for the right. You'll notice an interesting PATTERN.
3(x+4) + 4(x+3) 2(x+5) + 5(x+2)
------------- = ----------------
(x+3)(x+4) (x+2)(x+5)
7x + 24 7x + 20
------------- = --------------
x^2 + 7x + 12 x^2 + 7x + 10
Notice how the numerators and denominators have several things in common? That means when you cross-multiply, many of the terms will cancel out.
After cross-multiplying, simplifying, and canceling out terms, you'll get....
4x^2 + 14x = 0
2x(2x + 7) = 0
x = 0, -7/2
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
I think that the question is supposed to be this:
3/(x+3) + 4/(x+4) = 2/(x+2) + 5/(x+5) x = ?
13/4
-5/2
-7/2
9/2
17/2
I've come to a solution by using the following math steps:
First, set a common denominator for the left and a separate common denominator for the right. You'll notice an interesting PATTERN.
3(x+4) + 4(x+3) 2(x+5) + 5(x+2)
------------- = ----------------
(x+3)(x+4) (x+2)(x+5)
7x + 24 7x + 20
------------- = --------------
x^2 + 7x + 12 x^2 + 7x + 10
Notice how the numerators and denominators have several things in common? That means when you cross-multiply, many of the terms will cancel out.
After cross-multiplying, simplifying, and canceling out terms, you'll get....
4x^2 + 14x = 0
2x(2x + 7) = 0
x = 0, -7/2
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
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pitta.deepak
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Step 1: 3/(x+3) + 4/(x+4) = 2/(x+2) + 5/(x+5)
Step 2: 3/(x+3) - 2/(x+2) = 5/(x+5)- 4/(x+4)
Step 3: x/(x+3)(x+2) = x/(x+5)(x+4)
Step 4: (x+3)(x+2) = (x+5)(x+4)
Step 5: Simplify to get x= -7/2
Step 2 is crucial to solve it faster.
Step 2: 3/(x+3) - 2/(x+2) = 5/(x+5)- 4/(x+4)
Step 3: x/(x+3)(x+2) = x/(x+5)(x+4)
Step 4: (x+3)(x+2) = (x+5)(x+4)
Step 5: Simplify to get x= -7/2
Step 2 is crucial to solve it faster.
